Hi
if he is traveling by air yes he will need it, if he is driving across american border then no he wont need it yet, are you doing inland app? if you are then i dont think you can leave before getting ur passport stamped or risk of not being able to get back in but i dont know ur situation or which application you filed.
He is a UK citizen, so he requires his passport to enter the US and also to fly. It appears that they have submitted an overseas spousal application to London.
PMM